Testing the effect of deviance on similarity-based structure and certainty.
Hypothesis: We predict that as a new agent’s deviance from the group stereotype increases there will be a transition from group updating to subgroup formation to subtype formation. This will be reflected in participants’ similarity-rating derived dendrograms.
Method changes:
6 agents, 12 issues
introductory instructions prompt amended with “… complete a group impressions task…” and “… try to see if you can figure out to what extent each person agrees with everyone else in the group.”
PNS scale added
Note: data for prediction values are corrected in R script due to coding error
| 0 (N=54) |
0.25 (N=48) |
0.5 (N=59) |
0.75 (N=50) |
1 (N=67) |
Overall (N=278) |
|
|---|---|---|---|---|---|---|
| age | ||||||
| Mean (SD) | 37.2 (15.3) | 35.5 (14.3) | 35.7 (14.9) | 36.6 (14.0) | 36.9 (13.7) | 36.4 (14.4) |
| Median [Min, Max] | 35.5 [19.0, 73.0] | 32.0 [19.0, 73.0] | 31.0 [18.0, 78.0] | 33.0 [18.0, 69.0] | 34.0 [19.0, 73.0] | 33.5 [18.0, 78.0] |
| race | ||||||
| American Indian or Alaska Native | 1 (1.9%) | 1 (2.1%) | 0 (0%) | 0 (0%) | 0 (0%) | 2 (0.7%) |
| Asian | 5 (9.3%) | 7 (14.6%) | 6 (10.2%) | 6 (12.0%) | 6 (9.0%) | 30 (10.8%) |
| Black or African-American | 3 (5.6%) | 4 (8.3%) | 6 (10.2%) | 3 (6.0%) | 10 (14.9%) | 26 (9.4%) |
| Hispanic/Latinx | 1 (1.9%) | 0 (0%) | 4 (6.8%) | 1 (2.0%) | 5 (7.5%) | 11 (4.0%) |
| White | 44 (81.5%) | 35 (72.9%) | 43 (72.9%) | 40 (80.0%) | 46 (68.7%) | 208 (74.8%) |
| Other | 0 (0%) | 1 (2.1%) | 0 (0%) | 0 (0%) | 0 (0%) | 1 (0.4%) |
| gender | ||||||
| Man | 29 (53.7%) | 18 (37.5%) | 33 (55.9%) | 24 (48.0%) | 30 (44.8%) | 134 (48.2%) |
| Woman | 25 (46.3%) | 29 (60.4%) | 24 (40.7%) | 24 (48.0%) | 34 (50.7%) | 136 (48.9%) |
| Non-binary | 0 (0%) | 1 (2.1%) | 1 (1.7%) | 1 (2.0%) | 3 (4.5%) | 6 (2.2%) |
| Prefer not to answer | 0 (0%) | 0 (0%) | 1 (1.7%) | 1 (2.0%) | 0 (0%) | 2 (0.7%) |
| 0 (N=8) |
0.25 (N=1) |
0.5 (N=5) |
0.75 (N=5) |
1 (N=3) |
Overall (N=22) |
|
|---|---|---|---|---|---|---|
| age | ||||||
| Mean (SD) | 51.3 (14.9) | 22.0 (NA) | 35.6 (17.5) | 53.4 (14.7) | 45.0 (14.9) | 46.0 (16.5) |
| Median [Min, Max] | 50.0 [35.0, 69.0] | 22.0 [22.0, 22.0] | 27.0 [21.0, 57.0] | 62.0 [35.0, 66.0] | 51.0 [28.0, 56.0] | 50.0 [21.0, 69.0] |
| race | ||||||
| Asian | 1 (12.5%) | 0 (0%) | 1 (20.0%) | 0 (0%) | 0 (0%) | 2 (9.1%) |
| White | 7 (87.5%) | 1 (100%) | 1 (20.0%) | 5 (100%) | 2 (66.7%) | 16 (72.7%) |
| Black or African-American | 0 (0%) | 0 (0%) | 2 (40.0%) | 0 (0%) | 0 (0%) | 2 (9.1%) |
| Hispanic/Latinx | 0 (0%) | 0 (0%) | 1 (20.0%) | 0 (0%) | 0 (0%) | 1 (4.5%) |
| American Indian or Alaska Native | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 1 (33.3%) | 1 (4.5%) |
| gender | ||||||
| Man | 2 (25.0%) | 0 (0%) | 1 (20.0%) | 3 (60.0%) | 1 (33.3%) | 7 (31.8%) |
| Woman | 6 (75.0%) | 1 (100%) | 4 (80.0%) | 2 (40.0%) | 2 (66.7%) | 15 (68.2%) |
Analysis of Deviance Table (Type II Wald chisquare tests)
Response: corrresp
Chisq Df Pr(>Chisq)
opinion_round 220.9743 1 < 2.2e-16 ***
Deviant_threshold 51.3731 4 1.865e-10 ***
opinion_round:Deviant_threshold 4.7015 4 0.3193
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 1 opinion_round.trend SE df asymp.LCL asymp.UCL z.ratio p.value
overall 0.119 0.00799 Inf 0.103 0.134 14.873 <.0001
Results are averaged over the levels of: Deviant_threshold
Confidence level used: 0.95 $emmeans
Deviant_threshold emmean SE df asymp.LCL asymp.UCL z.ratio p.value
0 1.602 0.0994 Inf 1.407 1.797 16.111 <.0001
0.25 1.012 0.1014 Inf 0.814 1.211 9.980 <.0001
0.5 0.786 0.0906 Inf 0.608 0.963 8.674 <.0001
0.75 0.849 0.0983 Inf 0.657 1.042 8.641 <.0001
1 0.766 0.0851 Inf 0.600 0.933 9.009 <.0001
Results are given on the logit (not the response) scale.
Confidence level used: 0.95
$contrasts
contrast estimate SE df asymp.LCL
Deviant_threshold0 - Deviant_threshold0.25 0.5896 0.142 Inf 0.203
Deviant_threshold0 - Deviant_threshold0.5 0.8166 0.134 Inf 0.450
Deviant_threshold0 - Deviant_threshold0.75 0.7527 0.140 Inf 0.372
Deviant_threshold0 - Deviant_threshold1 0.8358 0.131 Inf 0.480
Deviant_threshold0.25 - Deviant_threshold0.5 0.2270 0.136 Inf -0.144
Deviant_threshold0.25 - Deviant_threshold0.75 0.1631 0.141 Inf -0.222
Deviant_threshold0.25 - Deviant_threshold1 0.2462 0.132 Inf -0.114
Deviant_threshold0.5 - Deviant_threshold0.75 -0.0639 0.134 Inf -0.428
Deviant_threshold0.5 - Deviant_threshold1 0.0193 0.124 Inf -0.319
Deviant_threshold0.75 - Deviant_threshold1 0.0831 0.130 Inf -0.271
asymp.UCL z.ratio p.value
0.976 4.159 0.0003
1.183 6.081 <.0001
1.134 5.390 <.0001
1.192 6.402 <.0001
0.598 1.671 0.4522
0.548 1.155 0.7767
0.607 1.863 0.3378
0.300 -0.478 0.9893
0.358 0.155 0.9999
0.437 0.640 0.9685
Results are given on the log odds ratio (not the response) scale.
Confidence level used: 0.95
Conf-level adjustment: tukey method for comparing a family of 5 estimates
P value adjustment: tukey method for comparing a family of 5 estimates Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
targetpair 103 103 1 278 0.406 0.5245
Deviant_threshold 71505 71505 1 278 282.971 <2e-16 ***
targetpair:Deviant_threshold 32839 32839 1 278 129.955 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1$emtrends
targetpair Deviant_threshold.trend SE df lower.CL upper.CL t.ratio p.value
DN -60.1 3.22 278 -66.4 -53.73 -18.650 <.0001
NN -11.7 2.78 278 -17.2 -6.24 -4.212 <.0001
Degrees-of-freedom method: satterthwaite
Confidence level used: 0.95
$contrasts
contrast estimate SE df lower.CL upper.CL t.ratio p.value
DN - NN -48.4 4.24 278 -56.7 -40 -11.400 <.0001
Degrees-of-freedom method: satterthwaite
Confidence level used: 0.95 Analysis of Variance Table
Response: k
Df Sum Sq Mean Sq F value Pr(>F)
Deviant_threshold 4 35.273 8.8183 15.948 9.56e-12 ***
Residuals 273 150.955 0.5529
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1$emmeans
Deviant_threshold emmean SE df lower.CL upper.CL t.ratio p.value
0 1.72 0.1012 273 1.52 1.92 17.002 <.0001
0.25 1.75 0.1073 273 1.54 1.96 16.316 <.0001
0.5 1.88 0.0968 273 1.69 2.07 19.414 <.0001
0.75 2.33 0.1052 273 2.12 2.54 22.147 <.0001
1 2.59 0.0908 273 2.41 2.77 28.543 <.0001
Confidence level used: 0.95
$contrasts
contrast estimate SE df lower.CL
Deviant_threshold0 - Deviant_threshold0.25 -0.0307 0.148 273 -0.436
Deviant_threshold0 - Deviant_threshold0.5 -0.1590 0.140 273 -0.544
Deviant_threshold0 - Deviant_threshold0.75 -0.6085 0.146 273 -1.009
Deviant_threshold0 - Deviant_threshold1 -0.8725 0.136 273 -1.246
Deviant_threshold0.25 - Deviant_threshold0.5 -0.1283 0.145 273 -0.525
Deviant_threshold0.25 - Deviant_threshold0.75 -0.5778 0.150 273 -0.990
Deviant_threshold0.25 - Deviant_threshold1 -0.8418 0.141 273 -1.228
Deviant_threshold0.5 - Deviant_threshold0.75 -0.4495 0.143 273 -0.842
Deviant_threshold0.5 - Deviant_threshold1 -0.7135 0.133 273 -1.078
Deviant_threshold0.75 - Deviant_threshold1 -0.2640 0.139 273 -0.646
upper.CL t.ratio p.value
0.374 -0.208 0.9996
0.226 -1.135 0.7876
-0.208 -4.169 0.0004
-0.499 -6.416 <.0001
0.269 -0.888 0.9012
-0.165 -3.845 0.0014
-0.456 -5.987 <.0001
-0.057 -3.145 0.0157
-0.349 -5.374 <.0001
0.118 -1.900 0.3198
Confidence level used: 0.95
Conf-level adjustment: tukey method for comparing a family of 5 estimates
P value adjustment: tukey method for comparing a family of 5 estimates Deviant_threshold emmean SE df null t.ratio p.value
0 1.72 0.1012 273 2 -2.762 0.0031
0.25 1.75 0.1073 273 2 -2.319 0.0106
0.5 1.88 0.0968 273 2 -1.245 0.1071
0.75 2.33 0.1052 273 2 3.128 0.9990
1 2.59 0.0908 273 2 6.527 1.0000
P values are left-tailed # A tibble: 2 × 13
model term estimate std.error statistic p.value conf.low
<chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
1 below_.5 Deviant_threshold -26.2 10.5 -2.50 0.0135 -47.0
2 above_.5 Deviant_threshold -3.41 10.3 -0.330 0.742 -23.8
conf.high r.squared adj.r.squared df df.residual nobs
<dbl> <dbl> <dbl> <dbl> <int> <int>
1 -5.49 0.0378 0.0317 1 159 161
2 17.0 0.000627 -0.00512 1 174 176Analysis of Variance Table
Response: confidence
Df Sum Sq Mean Sq F value Pr(>F)
deviance 4 7630 1907.59 2.3537 0.05425 .
Residuals 273 221253 810.45
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1$emmeans
deviance emmean SE df lower.CL upper.CL t.ratio p.value
0 60.4 3.87 273 52.8 68.1 15.598 <.0001
0.25 52.6 4.11 273 44.5 60.7 12.797 <.0001
0.5 47.3 3.71 273 40.0 54.6 12.754 <.0001
0.75 52.3 4.03 273 44.4 60.2 12.995 <.0001
1 45.8 3.48 273 38.9 52.6 13.162 <.0001
Confidence level used: 0.95
$contrasts
contrast estimate SE df lower.CL upper.CL t.ratio
deviance0 - deviance0.25 7.843 5.65 273 -7.666 23.35 1.389
deviance0 - deviance0.5 13.155 5.36 273 -1.568 27.88 2.454
deviance0 - deviance0.75 8.106 5.59 273 -7.237 23.45 1.451
deviance0 - deviance1 14.650 5.21 273 0.353 28.95 2.814
deviance0.25 - deviance0.5 5.312 5.53 273 -9.884 20.51 0.960
deviance0.25 - deviance0.75 0.263 5.75 273 -15.534 16.06 0.046
deviance0.25 - deviance1 6.807 5.38 273 -7.976 21.59 1.264
deviance0.5 - deviance0.75 -5.049 5.47 273 -20.076 9.98 -0.923
deviance0.5 - deviance1 1.495 5.08 273 -12.462 15.45 0.294
deviance0.75 - deviance1 6.544 5.32 273 -8.066 21.15 1.230
p.value
0.6354
0.1045
0.5954
0.0416
0.8727
1.0000
0.7132
0.8880
0.9984
0.7339
Confidence level used: 0.95
Conf-level adjustment: tukey method for comparing a family of 5 estimates
P value adjustment: tukey method for comparing a family of 5 estimates | 0 (N=54) |
0.25 (N=48) |
0.5 (N=59) |
0.75 (N=50) |
1 (N=67) |
Overall (N=278) |
|
|---|---|---|---|---|---|---|
| pred_maj | ||||||
| Yes | 47 (87.0%) | 43 (89.6%) | 45 (76.3%) | 43 (86.0%) | 47 (70.1%) | 225 (80.9%) |
| No | 7 (13.0%) | 5 (10.4%) | 14 (23.7%) | 7 (14.0%) | 18 (26.9%) | 51 (18.3%) |
| Missing | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 2 (3.0%) | 2 (0.7%) |
# A tibble: 4 × 14
# Groups: pred_maj [2]
pred_maj id term estimate std.error statistic p.value
<lgl> <chr> <chr> <dbl> <dbl> <dbl> <dbl>
1 FALSE below_.5 Deviant_threshold -19.7 24.8 -0.796 0.434
2 FALSE above_.5 Deviant_threshold 43.3 19.1 2.27 0.0294
3 TRUE below_.5 Deviant_threshold -21.3 11.1 -1.92 0.0571
4 TRUE above_.5 Deviant_threshold -16.5 11.8 -1.40 0.163
conf.low conf.high r.squared adj.r.squared df df.residual nobs
<dbl> <dbl> <dbl> <dbl> <dbl> <int> <int>
1 -70.9 31.4 0.0257 -0.0149 1 24 26
2 4.59 82.0 0.122 0.0982 1 37 39
3 -43.2 0.651 0.0269 0.0196 1 133 135
4 -39.9 6.78 0.0146 0.00716 1 133 135Analysis of Variance Table
Response: confidence
Df Sum Sq Mean Sq F value Pr(>F)
deviance 4 7282 1820.6 2.3898 0.0512800 .
pred_maj 1 10112 10112.2 13.2737 0.0003235 ***
deviance:pred_maj 4 7652 1912.9 2.5110 0.0422214 *
Residuals 266 202645 761.8
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1| 0 (N=54) |
0.25 (N=48) |
0.5 (N=59) |
0.75 (N=50) |
1 (N=67) |
Overall (N=278) |
|
|---|---|---|---|---|---|---|
| pns_med | ||||||
| High | 30 (55.6%) | 20 (41.7%) | 19 (32.2%) | 22 (44.0%) | 29 (43.3%) | 120 (43.2%) |
| Low | 24 (44.4%) | 28 (58.3%) | 40 (67.8%) | 28 (56.0%) | 38 (56.7%) | 158 (56.8%) |
# A tibble: 4 × 14
# Groups: pns_med [2]
pns_med id term estimate std.error statistic p.value
<chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl>
1 High below_.5 Deviant_threshold -42.5 14.9 -2.86 0.00567
2 High above_.5 Deviant_threshold 9.33 16.2 0.577 0.566
3 Low below_.5 Deviant_threshold -6.71 14.8 -0.454 0.651
4 Low above_.5 Deviant_threshold -14.7 13.2 -1.11 0.268
conf.low conf.high r.squared adj.r.squared df df.residual nobs
<dbl> <dbl> <dbl> <dbl> <dbl> <int> <int>
1 -72.2 -12.8 0.109 0.0954 1 67 69
2 -22.9 41.6 0.00487 -0.00977 1 68 70
3 -36.1 22.6 0.00229 -0.00880 1 90 92
4 -40.8 11.5 0.0118 0.00226 1 104 106Analysis of Variance Table
Response: confidence
Df Sum Sq Mean Sq F value Pr(>F)
deviance 4 7630 1907.6 2.4332 0.047819 *
pns_med 1 8280 8279.7 10.5609 0.001303 **
deviance:pns_med 4 2863 715.8 0.9130 0.456789
Residuals 268 210110 784.0
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1| 0 (N=278) |
1 (N=278) |
2 (N=278) |
3 (N=278) |
4 (N=278) |
5 (N=278) |
6 (N=278) |
7 (N=278) |
8 (N=278) |
9 (N=278) |
10 (N=278) |
11 (N=278) |
Overall (N=3336) |
|
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| trialnum | |||||||||||||
| 0 | 47 (16.9%) | 44 (15.8%) | 46 (16.5%) | 59 (21.2%) | 37 (13.3%) | 48 (17.3%) | 39 (14.0%) | 38 (13.7%) | 40 (14.4%) | 40 (14.4%) | 54 (19.4%) | 49 (17.6%) | 541 (16.2%) |
| 1 | 46 (16.5%) | 42 (15.1%) | 50 (18.0%) | 41 (14.7%) | 51 (18.3%) | 38 (13.7%) | 41 (14.7%) | 58 (20.9%) | 41 (14.7%) | 41 (14.7%) | 37 (13.3%) | 50 (18.0%) | 536 (16.1%) |
| 2 | 56 (20.1%) | 51 (18.3%) | 44 (15.8%) | 50 (18.0%) | 45 (16.2%) | 53 (19.1%) | 40 (14.4%) | 40 (14.4%) | 56 (20.1%) | 43 (15.5%) | 44 (15.8%) | 54 (19.4%) | 576 (17.3%) |
| 3 | 34 (12.2%) | 37 (13.3%) | 43 (15.5%) | 42 (15.1%) | 50 (18.0%) | 50 (18.0%) | 50 (18.0%) | 40 (14.4%) | 46 (16.5%) | 33 (11.9%) | 44 (15.8%) | 33 (11.9%) | 502 (15.0%) |
| 4 | 50 (18.0%) | 55 (19.8%) | 57 (20.5%) | 38 (13.7%) | 56 (20.1%) | 51 (18.3%) | 59 (21.2%) | 54 (19.4%) | 43 (15.5%) | 58 (20.9%) | 48 (17.3%) | 36 (12.9%) | 605 (18.1%) |
| 5 | 45 (16.2%) | 49 (17.6%) | 38 (13.7%) | 48 (17.3%) | 39 (14.0%) | 38 (13.7%) | 49 (17.6%) | 48 (17.3%) | 52 (18.7%) | 63 (22.7%) | 51 (18.3%) | 56 (20.1%) | 576 (17.3%) |